Find an equation for the conic whose graph is shown.
A) $\frac { y ^ { 2 } } { 9 } - \frac { x ^ { 2 } } { 25 } = 1$
B) $\frac { y ^ { 2 } } { 25 } - \frac { x ^ { 2 } } { 16 } = 1$
C) $\frac { y ^ { 2 } } { 9 } - \frac { x ^ { 2 } } { 16 } = 1$
D) $\frac { x ^ { 2 } } { 9 } - \frac { y ^ { 2 } } { 25 } = 1$
E) $9 y ^ { 2 } - \frac { x ^ { 2 } } { 16 } = 1$

Question

Find an equation for the conic whose graph is shown. 
A) $\frac { y ^ { 2 } } { 9 } - \frac { x ^ { 2 } } { 25 } = 1$ 
B) $\frac { y ^ { 2 } } { 25 } - \frac { x ^ { 2 } } { 16 } = 1$ 
C) $\frac { y ^ { 2 } } { 9 } - \frac { x ^ { 2 } } { 16 } = 1$ 
D) $\frac { x ^ { 2 } } { 9 } - \frac { y ^ { 2 } } { 25 } = 1$ 
E) $9 y ^ { 2 } - \frac { x ^ { 2 } } { 16 } = 1$

Quizplus · Accepted Answer

The graph is a hyperbola because it has two distinct branches and it is centered at the origin. Also, the branches open horizontally, so the x-term should be subtracted. The standard form equation for a hyperbola with these characteristics is $\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$, where $a$ is the distance from the center to each vertex along the x-axis and $b$ is the distance from the center to each vertex along the y-axis. From the graph, we can see that $a=4$ and $b=3$, so substituting these values gives us $\frac{x^2}{16}-\frac{y^2}{9}=1$. Simplifying, we get $\frac{y^2}{9}-\frac{x^2}{16}=1$, which matches choice C. Therefore, the answer is C.

Find an Equation for the Conic Whose Graph Is Shown y29−x225=1\frac { y ^ { 2 } } { 9 } - \frac { x ^ { 2 } } { 25 } = 19y2​−25x2​=1

Find an Equation for the Conic Whose Graph Is Shown $\frac { y ^ { 2 } } { 9 } - \frac { x ^ { 2 } } { 25 } = 1$